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Abstract

In this study, we implement a matrix calculation system in Maxima (GNU) based on the numerical integration of flexibility terms to obtain fixed-end rotation, fixed-end moments and the entries of the T-beams stiffness matrix with linear haunches. We took into account the shear and axial deformations that are not included in formulations of packages for broadly used structural calculation on a global scale as SAP2000. All of this, to demonstrate that a systematic and reasonable standard-setting calculation methodology based on numerical integration can match the results obtained from robust finite element tools, being this methodology a more economical option because of its low computational cost. For this matter, the numerical integrals of the flexibility and rotation factors of Tena-Colunga were calculated approximatively, implementing three-point Gauss quadrature’s, Taylor polynomial and Romberg, with the help of the Computational Algebra System Maxima (GNU) for tapered forms of T-beams. We established a comparison with the formulations used by the finite element packages Ansys® and SAP2000® and we validated the results with identical models made in these two packages. Efficacy and precision of the developed model were verified by using this approach, and we concluded that this methodology represents significant advantages in the structural calculation of tapered beams with linear haunches.